Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.17700 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911396977967104 |
|---|---|
| author | Deng, Li Li, Xin |
| author_facet | Deng, Li Li, Xin |
| contents | This paper studies the uniformly asymptotic stability of nonautonomous systems on Riemannian manifolds. We establish corresponding Lyapunov-type theorems (Theorems 2.1 and 2.2), extending classical Euclidean results (e.g., [9, Theorems 4.9 and 4.10]) to curved spaces. Our main contributions are: (i) an estimate for the domain of attraction linked to the equilibrium point's injectivity radius, where, under suitable conditions, this radius can be bounded using the sectional curvature (Proposition 2.1); (ii) a demonstration that this estimate depends on the choice of the Riemannian metric (Examples 2.1 and 2.2 and Remark 2.4); and (iii) a refined estimate compared to the Euclidean case, as detailed in item (6) of Remark 2.1 and in Remark 2.3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17700 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lyapunov Stability for nonautonomous systems on Manifolds Deng, Li Li, Xin Dynamical Systems This paper studies the uniformly asymptotic stability of nonautonomous systems on Riemannian manifolds. We establish corresponding Lyapunov-type theorems (Theorems 2.1 and 2.2), extending classical Euclidean results (e.g., [9, Theorems 4.9 and 4.10]) to curved spaces. Our main contributions are: (i) an estimate for the domain of attraction linked to the equilibrium point's injectivity radius, where, under suitable conditions, this radius can be bounded using the sectional curvature (Proposition 2.1); (ii) a demonstration that this estimate depends on the choice of the Riemannian metric (Examples 2.1 and 2.2 and Remark 2.4); and (iii) a refined estimate compared to the Euclidean case, as detailed in item (6) of Remark 2.1 and in Remark 2.3. |
| title | Lyapunov Stability for nonautonomous systems on Manifolds |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2601.17700 |